Miscellaneous Calculations
This page is to talk about and show calculations that are of different measurements besides kinetic and potential energy. Bekenstein Limit This is to calculate how much maximum amount of information there is in a certain space before becoming a black hole. With this, can you find how much mass and/or energy there is for stat for intelligence or information processing. Here are some of the components for the formulas: * I = Information (bits) * R = Radius (meters) * m = Mass (kilograms) * ħ'' = reduced Planck constant (1.054571800e-34 J/s) * c = speed of light (299792458 m/s) * ''ħc ''= reduced Planck constant (3.16152649e-26 J/m) * ln = natural logarithm (log) * E = energy (Joules) For Mass formula: (2*pi*299792458*R*m/1.054571800e-34*log(2)) For Energy formula: (2*pi*R*E/3.16152649e-26*log(2)) Or to find Energy from Information: I/(2*pi*R/3.16152649e-26log(2)) Black Hole Creation The good thing is that there is an easy formula that lets us approximate the mass of black holes based on the radius of the event horizon. It is: ''r''s = 2*G*M/c^2 where: : ''r''s is the Schwarzschild radius (radius of the event horizon); : G is the gravitational constant; : M is the mass of the object; : c is the speed of light in vacuum. A more comfortable way may be calculators for the mass and size of a black hole such as this one or this one. In order for it to be considered a true black hole, it must follow most of the following: * Black holes cannot be destroyed with brute force, because they will simply absorb all energy/matter thrown at them, and grow larger, nor can they be physically interacted. * They are capable of easily destroying planets and stars (although with small black holes, it might take a while) * Black Holes are described as an infinite Gravity Well. * Black Holes stretch matter in a spaghetti like fashion. * Black holes do decay over time due to Hawking Radiation, so if you leave a black hole alone and don't feed it anything, it will eventually grow smaller and explode (this type of detonation is a 100% efficient mass - to - energy conversion, with more potential power than a nuke or antimatter explosive) * Tiny black holes with masses less than a few trillion tons would evaporate nearly instantly. Black holes with higher masses last much longer - a black hole with the mass of the sun, for example, would last for billions or trillions of years before evaporating. * Black Holes can absorb anything slower than FTL objects. The only way for Black Holes to be theorethically destroyed or avoid being caught in it are for the following, Exhausting all it’s mass in Hawking Radiation, Reality Warping or Extreme hax, moving faster than light to not get caught in it’s gravity. C.A.P.E. (Conventional Available Potential Energy) This calc page is for feats that are to find the energy of storms created. Variables First are the variables that would remain constant and would not change in any formula. * he storm is cylindrical in shape * Independent of how high it floats off the ground, the storm mass itself 30,000 ft tall, going by this. And with Cumulonimbus which have a thickness of about 8000m to 11800m * The distance to the horizon is the radius of the storm And some variables that would change depending on the feats. * Observer Height, and thus, distance to the horizon (here is a link for that) * Assumed Instability in Kilojoules Here are some set of values to finding the storms AP (via Kilojoules) in different settings: "Weak Instability" refers to a CAPE value of less than '''1 kj/kg', "Moderate Instability" means 1 to 2.5 kj/kg, and "Strong Instability" yields 2.5 to 4 kj/kg. Or some real life examples such as 5.89 Kj/kg - 1999 Oklahoma Tornado Outbreak and 8 Kj/kg - 1990 Plainfield Tornado. Volume of Cloud here is the equation to find the volume of the clouds by applying the above. V = (m^3) * 1.003 kg/m^3 * Instability Or... Volume = (Area in m^2 * (8000m or 11800m)) * 1.003 * CAPE pi = 3.14 Sum It All Up then apply the cloud density to the equation by multiplying the result by 1.003 (kilograms per cubic meter), then multiply the total mass by the CAPE values. in joules per kilogram (change the Kj to J, 1 kj = 1000 j). here is the other equation: ((pi * Horizon distance (in meters)^2 * 13,000 m) * 1.003) * CAPE (In j/kg). Compression This Calculation is for feats that involve compression of any scale. Here are a few things to find in order to get a reasonable formula: * Area (m^2) * thickness of the target (km) Multiply them together to get the volume of said target, after that find the size of what the target is after compression or information for accuracy, once done that, do the following: * Size * Volume = volume after compression Then you must find the compression value (minimum should be 69 MPa = 6.9e+7 N/m^2 = P) Then we need to find the difference in the two volumes pre and after compression (∆V) * Pre Volume - After Volume = Difference m^3 Now we need to multiply botht eh compression value with the difference in volume. * P*∆V=Nm (Newton Metre) Finally we find the the Energy value by converting the Newton to Joules. Decibel This page is to talk about how to find the energy in the calculation of the Decibels for Intensity and Pressure (The later is what is used for AP). First is the Intensity: * Find the number of decibels/watts you wish to convert * Once you found Watts, apply it to the following equation to (P2) to the right side * Then divide P2 with P1 (10^-12) * With the result, apply it to the log^10 * Then * by 10 to get the final result for # of decibels * You can apply this to find watts as well by doing the formula in reverse. Now for the Pressure * Find the number of decibels/pressure you wish to convert * Once you found pressure (Pa), apply it to the following equation (p'') to the right side * Then divide ''p by Pref (2.0x10^5) * With the result, apply it to the log^10 * Then * by 20 to get the final result for # of decibels * You can apply this to find the pressure by doing the equation in reverse * you can then convert pressure to newtons which is equal to Joule m^2. Durability This One I will do Later. Earthquake Bold textItalic textInternal linkExternal link (remember http:// prefix)Level 2 headlineEmbedded fileFile linkMathematical formula (LaTeX)Ignore wiki formattingYour signature with timestampHorizontal line (use sparingly)Add photovet-imagebuttonmore + Overview An earthquake (also known as a quake, tremor or temblor) is the perceptible shaking of the surface of the Earth. Earthquakes can be violent enough to toss people around and destroy whole cities. Such earthquakes being caused by characters are a method useable to determine Attack Potency. One has to differentiate between different ways an earthquake was caused, if one wants to calculate the energy. Case 1: Meteor impact This is the easiest method to determine the necessary energy to cause an earthquake, even though not the most commonly used one. In which cases should it be used? This method should be used if an earthquake is caused through the impact of a meteor or through an event very similar to that. How is it done? 'Step 1:' First step is to determine the distance of a place, for which we know which effects the earthquake had on, to the epicenter. To clarify: The epicenter is the point on the Earth's surface that is directly above the hypocenter or focus, the point where an earthquake or underground explosion originates. From the rest this calculator will be used. 'Step 2:' Input the distance from the epicenter, which was determined in Step 1, in the "Distance from Impact" field. After that input the rest of the values, for now it doesn't matter what stands in the rest of the fields. Press "calculate effects". If the inputs were sufficiently high on the page that appears will be a section named "Seismic effects". In that section descriptions are given which describe the effects of an earthquake, which was caused by a meteor with the properties described by the prior input. Specifically this are the effects at the input distance from the epicenter. All possible descriptions are listed in Table 1. What one now wants to do is to change the input values, except the "Distance from Impact" value, so long until you have the lowest values, for which still the description best fitting for the effects at your chosen distance from the epicenter is shown. 'Step 3:' If you have found this values take a look at the "Energy" section above the "Seismic Effects" section on the page. The value given for "Energy before atmospheric entry" is the energy of your (theoretical) meteor and with that also the energy of necessary to cause the earthquake. Case 2: Natural Earthquakes This method doesn't find much use, but is worth mentioning. In which cases should it be used? This method should only be used in case a natural earthquake occurs, as it takes into account the work necessary to overcome the friction between continent plates etc. How is it done? First perform step 1 and step 2 like described in "Case 1: Meteor Impacts". Since here one does not wish to know the energy necessary for a meteor, but for a real earthquake this time the third step has to be different. Instead of looking at the "Energy" section, one looks at the "Seismic Effects" section again. There a value named "Richter Scale Magnitude" will be listed. This is the magnitude an earthquake would need to have to cause the described effects at the distance from the epicenter we input. The value is independent from the method through which the earthquake was caused, so it also stays true for other natural earthquakes which aren't caused by meteor impacts. One takes the Richter Scale Magnitude and inputs it in this calculator in the "Earthquake Magnitude" field. Then press the compute button. The value for "Total "Seismic Moment Energy" (MO)" is the energy necessary to cause such an earthquake. Case 3: Other This is the most common method to calculate earthquakes. In which cases should it be used? This should be used if the earthquake is not caused through something very similar to a meteor impact and is also not a natural earthquake. How is it done? The method is identical to that of "Case 2: Natural Earthquakes", just this time instead of the "Total Seismic Moment Energy" (MO)" value our end result is the "Seismic Energy in Waves Radiated from Earthquake Source" value. The reason one uses that value in this case is that the big energy loss that comes through the movement of the continental plate or similar processes of natural earthquakes is not present here. Instead we can only use the amount of energy that actually takes part in the effects we observer. Hence only the energy radiated in form of seismic waves is relevant for this case. Use this as a reference for Earthquake power chart. Or this to get both the formula and richter scale magnetude. A description of magnitude's capabilities. Simplify Here is the calculation simplified: M = log10(mm)+3*log10(8*t)-2.92 *t = time difference (distance by miles divided by 5.7) *mm = amplitude (It is amplified by x10 for each 1 magnitude increase using logarithmic) **2.5 = 50 mm, you can use this for reference to multiply Map Size This page is for working to find the size of the map or location that you are trying to make, these steps will help you to do so. First find an app or program that is good with pixel measurement such as GIMP or photoshop, then find images that would connect to one another. It is good to start with what is small then work your way up on size comparison. Second Find a reliable source for reference from said series, or use a reliable source for average size of for example a human male. then use that as a basis. Third Then you use pixel lines to measure from smallest thing with reference then star working your way up with size comparison until you finally reach the area you want to find the size of. Sites Here are a few sights to help your find the area of an area, facility, settlement, building, large vehicle or celestial body. * https://www.freemaptools.com/area-calculator.htm * http://www.1728.org/angsize.htm * http://www.calculator.net/area-calculator.html * https://anatomy4sculptors.com/hpc Freezing Energy This page is to find the energy for feats that causes freezing or creations of large polar bodies, here are the following steps for that. * First, find the the volume (m^3), density (kg/m^3), and then multiply both to find the mass (kg). * Then find the mass of the atmospheric composition of area by dividing it by the percentage of each elemental compounds. Then multiply separately each compound percentage with the both the original volume and density to get the mass. * Now things get more complicated as it requires you to find the following for each elemental compound to get the answer you seek. ** air temperature (Kelvin) ** specific heat (j/kgk) ** Boiling point (kelvin) Then do the following equation with the values above with the specific compound (mass (kg) * specific heat (j/kgk) * ( air temperature (K) - boiling point (K)) = Joules *use this website to help when you have gathered information on a compound: https://www.omnicalculator.com/physics/specific-heat * repeat this process for each atmospheric compound Now for each compound you must find the following: ** Vaporization Heat j/kg *** Then multiply that to original mass of the specific compound to get Joules ** Melting point Kelvin *** use the first formula with the mass * specific heat * (air temperature - boiling point) except replace boiling point with melting temperature to get Joules. ** Fusion Heat j/kg *** Multiply that with the mass of the specific compound to get joules Now add all the four total number of joules together to get the total energy for that specific atmospheric compound, repeat the previous process for the remaining compounds Finally once you have all the total energy for each atmospheric compound, add them all up together and you will have the total energy use seek. Height, Length, Depth, Volume, Angel Measurement This is to talk about the measurement of the Depth of any DC feat which is using various factors such as length, width, height of any elevated geographic structure, angle of the shadows in the crater. This falls under certain steps in process such as the First Step. # First is finding the width and length (meters) of the end feat. # Then we measure the max height of the geographic elevation. Step 2) Below is the way to look at how to measure the angle of the shadows. So the basic of the calculations is this in order # Measure a triangular shape by first drawing a line from where the shadow is cast, then line down to the edge of the crater is (height) then connect the lines (Length) to form a type of Scalene Triangle. Here is a link for examples of shadow angles. # Length / Height = width of the shadow than convert to angular degree. # width (From first step) * angle of the Shadow # Afterward add the height of the geographic elevation (height step 1) + total depth (or not for low end) Step 3) Next is to find the closest volume for calculations (Use the most accurate prism for this case then add the depth): # Find the Width, Length then add the depth. # Then multiply all three to get the volume by m^3 (if measuring by meters) # then Multiply by method of destruction. Then you mad convert them to get the estimated result. Image Angle If push comes to shove, you can use the following site for angle/distance and size For any other means to find an object size or distance from certain points in a scene, first and foremost is to do pixel measurements and finding information to best determine the object's size or distance or an estimate for the average size of something that is related to it. * First find the px number of both the height of the screen and the diameter of the object, then apply the info to the equation below ** 2atan(tan(70 / 2)(object px / screen px) *** After that, convert the result from Radian to Degrees and you will get the result of degrees. *** Then use the website above for angle/distance/size to find one of the following with the other two units of info. Luminosity Energy This is to help estimate the energy released from any body via Luminosity, To do that we need a few things: Her is the equation to help move things along: (o*t^4)*(4*pi*r^2)=L: *O is the Stefan Boltzmann constant (5.670373e-8 W m-2 K-4) *t is the Temperature *r is the radius of the body (meters) *L is the Luminosity Total (watts=Joules) You then convert the Joules per Second to Tons, and then multiply it by the area of the star to find the Energy of TNT to Tons per m^2 to get the Intensity. The temperature of any given star, including a neutron star, is determined by using Wien's displacement law, which states that the wavelength is equal to the displacement constant (a value equal to 2900 micro''meters per Kelvin, or about 2.897 7729(17)e-13 meters per Kelvin) divided by the temperature. So, in order to get the temperature, we need to do a quadratic equation; we divide the wavelength by the Wien constant. '''EX.' The maximum wavelength of a neutron star is 2.9 nanometers, or 0.0029 micrometers. The constant, as I said above, is 2900 micrometers per Kelvin. *Tk = 2900Mm/0.0029 = 1,000,000 kelvins Radiation Energy This is to help those who have temperature questions that wish to calculate that to actual feats or stats. the link below would help with finding the number for joules, this requires: * Emissivity * Surface Area * Temperature Here is the link for that simplified equation: *http://www.endmemo.com/physics/radenergy.php Here is the functions on how to find them *Area: 2 π r^2 + 2 π r h *emissivity: http://www.infrared-thermography.com/material.htm *Temperature: what is being discussed Speed & Cinematic/Comic Time This Page is for calculating the speed of characters, attacks and vehicles, through various means such as physical speed, teleportation speed, engine speed, speed via powers. The standard calculation of speed involves the classic Time/Speed/Distance formula. For the speed of other means or for more details such as powered jumps, flight, swimming, etc. must require more factors such as strength of jumps, their height and landing, etc.. This can be calced for both, regular speed, combat speed or reaction speed. For Speed from a video or comic/manga and not a map, if there is no accurate distance/time/speed labeled, go to the Image Angle above to find the size of any location on any screen/panel and the size of the object (km) via pixel measurements and measure how much time passed between both points of movement. * after you find the distance between both points (km) before and after, You then take take those points and minus them. * When you find how much time has past (seconds), find the frames per second on a video and how many seconds it takes and multiply them together to find the fps. * For panels, this one is a bit tricky, you can use the Syllable counter or this link which is average speaking speed of 4-5 syllables per second. as for panels that have no dialogue, that is a tricky scenario, you would honestly have to use your best judgement, in other websites they say the average is between 10-15 seconds, but again, use best judgement. * Once you find the time in either scenario, you then take the distance between the two points (km) and divide by time (seconds) to get the speed (m/s). Although such cases exist, cinematic time can be used to determine time-frames for calculations, such as this calc, or the Pumpkin speed calchere. Surface Area of Beings this is a page to calculate the surface area of any living being with certain requirements. here is the site for making the calculation easier: halls.md/body-surface-area/bsa.htm but the basic requirements are height (cm) and weight (kg) to find the surface area (m^2) You can either use either of these methods to find the answer: * 0.20247*height in meters^0.725*(weight in kilograms)^0.425 = surface area in m² Anatomy Proportion Measurement Here is the website for anatomy proportion measurements * Anatomy Calculator NOTE: When using this for Other feats such as measuring it with attacks to determine durability or so, You must find the cross section between both the humanoid surface area and the area of the attack, usually the difference is 50% or so, thus the area should be around ~40% of the humanoid surface area. Temperature Change/Heat Capacity This page is to talk about found and calculating the change in temperatures and the heat capacity of certain substances. Temperature Change First you need to find the standard temperature of the sustance before you go for the changed temperature, then you find what the substance temeprature changes to. Then you take that and minus the original temp to find the change in temperature. We use the room temperature for average which is 21.1 celcius. Heat Capacity *We determine the energy given or taken in changing the temperature, the equation for this is E=m*c*ΔT *E is the energy (J) *m is mass (kg) *c is specific heat capacity (J/kgKorC), this varies between materials and is based on how much energy is required to get that material to a certain heat (if you put stone and steel over the same fire they will receive energy at the same rate but the steel will heat up faster) *ΔT is the change in temperature (Kelvin or Celcius) You can use this to either find the energy or specific heat. Vaporization and Melting Energy *We determine the energy given or taken in changing the state of matter (if the feat we are calculating did not involve a state change i.e. something being set on fire does not include a change of state, then we do simply perform this second step). *If the feat involved a change between solid and liquid (in either direction) we must multiply the mass of the material with the material's "heat of fusion". *If the feat involved a change between liquid and gas (in either direction) we must multiply the mass of the material with the material's "enthalpy of vaporisation", this varies based on atmospheric pressure. here are a few examples for specific information *Specific heat capacity of water is 4181J/kg°K *Heat of fusion for water is 334.16J/g Here a few pre-calculated example values (starting with the materials at 20°C): *Melting Granite: 4358.9475 J/cm^3 *Melting Cement: 12.232.65 J/cm^3 *Melting Glass: 2494 J/cm^3 *Freezing Water: 418 J/cm^3 *Vaporization of water: 2575 J/cm^3 *Vaporization of titanium: 49079.7 J/cc Here are a few websites to help with that. *thermodynamical energy constants for common substances *Vaporization_of_Titanium_Value *Specific Heat Calculator *search for Specific Heat in substances Water Body Creation This page is for feats which creates bodies of water, here are the steps to accomplish this. *first you need to find an accurate volume or size of the body of water in m^3 *Then find the density of the Water in kg/m^3 *Then multiply both to find the mass in kg *Then convert Kg to moles (There are 55.6 moles in 1 kg) *Then follow the enthalpy of the formation of water by multiplying the amount of moles form the previous step with 285800 J/mol. *Then you will have your answer. Watt/Voltage/Ampere This page is for the calculation of joules from watts/voltage/amperes, to do so, follow the Ohm's Law formula and these steps. * voltage/resistors(Ohms)=amps * Find the Voltage * Find the resistors (1 M Ohm = 1000000 Ohm) * then divide the two to get amps * then multiply the result with voltage to get watts which then becomes Joules. Technique Speed Technique Speed is a way of measuring the speed of an attack that has either been initially cast, how fast it travels and/or how fast it takes effect. *Water-cutting speed: ~1,020 m/s *Ablation speed: 2000 m/s *Meteor speed (Earth): 11,000 m/s *Electrical discharge: 60,000 m/s *Stepped Ladder Lightning: 150,000 m/s *Light: 299 792 458 m/s This may be involved in the use of TimeFrame. NOTE: For an attack to be Light speed if it is Light Base must follow at a minimum, a few of these criteria: *The beam refracts in a new material, such as a liquid or... *The beam reflects off a material that it can be expected to, such as a non-magical mirror *The beam is called lightspeed by credible scientific sources *It is stated to be made of photons or light itself, again by a credible scientific source *It has its origin at a realistic source of light, such as a camera Furthermore, there are a few criteria which show a beam is NOT real light: *It is shown at different speeds in the same material *It is tangible and can be interacted with physically by normal humans *They do not travel in straight lines (unless you can prove refraction/reflection, see above) NOTE: However, there maybe some exceptions if the light power in question comes from the same category of powers that are dubbed or proven as actual elements. Where the Laser may bend/curve depending on what type of medium it travels through (such as Atmospheric Refraction). In order to calc that though, you must do the following: # Find the degrees of the angel in which the laser bends or curves. # Then apply it to this calc, sin(# of degrees) = answer. # divide 1 by the answer from #2 above. # Then divide the speed of light (m/s) by the answer from #3. # Then calc that in m/s to Light Speed to get results. This part should be taken with extreme care and not be abused by simply saying this. Formula for Attack Dodging This can be used with the technique speed measurements above for dodging: \tfrac{\text{(Distance the character moved (m))} \times \text{(Speed of attacks (m/s))}}{ \text{Distance the attack was away at the point character started moving (m)}} = \text{Speed of character (m/s)} This would include various attack types such as lasers or lightning as well. Category:Information Category:Calculation